Fed X and DHL are both operating in Panama City. Our experience has been mixed. Things have never gotten lost, which is very good, but it may take a while the shipment to arrive. We have ordered medicine shipped in from China (cheap prices!) and had a bit of problem receiving it due to incorrect documentation from the shipper.
But with a little diligence we did receive our package. One of the things we experienced is as we have ordered the same meds from the same source the process went very smoothly on the consecutive times it was shipped.

One of the things we like about DHL here is they call you before they deliver, so you know the package is on the truck. They call for directions because unlike the states where every building has an assigned address, here it's more like the yellow building on Balboa beside Extreme Planet. What's also not like the states is it seems they don't deliver all the mail everyday. It seems when quitting time comes even if there are a few package to delivery...well that's all right, they will be there tomorrow and maybe they can get to it then. Latin American Mañana syndrome, you gotta love it or it will drive you crazy!

You can also arrange to have your shipment delivered to the closest office, they will call you and hold the package for pickup if you are in a real hurry.

Over all it's really just been one of those learning curves for us on how Panama does things and not to expect US responses for service and methods in a foreign country.